| Author(s) |
Du, Yihong
|
| Publication Date |
2008
|
| Abstract |
Let u∊ be a single layered radially symmetric unstable solution of the Allen-Cahn equation -∈²Δu=u(u-a(|x|))(1-u) over the unit ball with Neumann boundary conditions. Based on our estimate of the small eigenvalues of the linearized eigenvalue problem at u∊ when ∈ is small, we construct solutions of the form u∊ + v∊, with v∊ non-radially symmetric and close to zero in the unit ball except near one point x₀ such that |x₀| is close to a nondegenerate critical point of a(r). Such a solution has a sharp layer as well as a spike.
|
| Citation |
Journal of Differential Equations, 244(1), p. 117-169
|
| ISSN |
1090-2732
0022-0396
|
| Link | |
| Publisher |
Academic Press
|
| Title |
The heterogeneous Allen-Cahn equation in a ball: Solutions with layers and spikes
|
| Type of document |
Journal Article
|
| Entity Type |
Publication
|
| Name | Size | format | Description | Link |
|---|